Alexandrov immersed minimal tori in S^3

TL;DR

This paper proves that Alexandrov immersed minimal tori in the 3-sphere are necessarily rotationally symmetric, extending similar results to constant mean curvature surfaces.

Contribution

It establishes a symmetry result for Alexandrov immersed minimal tori in S^3, a novel classification in differential geometry.

Findings

Minimal tori in S^3 with Alexandrov immersion are rotationally symmetric

The result extends to constant mean curvature surfaces

Provides a classification of such surfaces based on symmetry

Abstract

We show that any minimal torus in $S^3$ which is Alexandrov immersed must be rotationally symmetric. An analogous result holds for surfaces of constant mean curvature.